Deliberate mistake: When the rocket (a replica of an Atlas booster) launches, it makes it all the way to orbit in one piece. In reality the Atlas was a two-stage rocket, and the first stage would've been jettisoned long before reaching orbital velocity. (Undoubtedly the filmmakers decided to fudge this, to avoid dealing with the issue that the rocket didn't launch over the ocean, and the first stage would've fallen onto some innocent bystander's property.).
The Astronaut Farmer (2006)
1 deliberate mistake - chronological order
Directed by: Michael Polish
Starring: Billy Bob Thornton, Bruce Dern, Virginia Madsen, Max Thieriot, Jasper Polish
Other mistake: During the credits, Jay Leno shakes Billy Bob Thorton's hand and then says "How are you Bob? Nice to see you". He should have called him Charlie or Farmer. (01:38:40)
Arnold 'Arnie' Milan: You got bad credit, but, uh, you got great character.
Trivia: The spacesuit that the character Charles Farmer wore is a replica of the pressure suit used by the Mercury 7 astronauts.